Dynamic Response of Stepped Beams Under Impulsive Loading

Aim To analyze dynamic failure of aerospace strutures subjected lateral impulsive loading. Methods Structures were modeled as rigid-perfectly plastic free-free stepped beams. Basic equations of motion un set up for analysis. Results Final pat deformation and rigid motion solutions were determined for a uniform impulsive loading. The critical rupture conditions for a space shuttle and a missile were obtained. Conclusion Failure is possible for aerospace structures under a uniform impulsive loading, but it is mere difficult in space.

尝试分析典型古建筑构件——斗拱的力学原理

斗拱是最能代表中国古代建筑艺术的构件.本文通过查找相关资料,请教专业技术人员,建立了简单的斗拱模型,分析了斗拱的力学原理,明确了斗拱的承重功能.并提出应在现代建筑的设计中充分借鉴中国古代建筑智慧,建造出更多独具中国特色的建筑.

Closed-form solution for shear lag effects of steel-concrete composite box beams considering shear deformation and slip

Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.

Numerical study of RC beams under various loading rates with LS-DYNA

Having an accurate understanding of concrete behavior under effects of high strain rate loading with the aim of reducing incurred damages is of great importance. Due to complexities and high costs of experimental research, numerical studies can be an appropriate alternative for experimental methods. Therefore, in this research capability of the finite element method for predicting concrete behavior at various loading conditions is evaluated by LS-DYNA software. First, the proposed method is presented and then is validated in three stages under different conditions. Results of load-lnidspan displacement showed good agreement between experimental and finite element results. Capability of finite element method in analyses of beams under various rates of loading was also validated by low error of the results. In addition, the proposed method has reasonable ability to evaluate reinforced concrete beams under various loading rates and different conditions.

Dynamic response of a beam on a Pasternak foundation and under a moving load

The dynamic response of an infinite beam placed on a Pasternak foundation when the system was subjected to a moving load was investigated.We used the double Fourier transform and its inversion to solve the formulations of the problem.A closed form analytic solution of the beam was obtained by the theorem of residues.We selected a numerical example to illustrate the dynamic response of the beam on Pasternak and Winkler foundations,respectively.We discuss the effect of the moving load velocity on the dynamic displacement response of the beam.The maximum deflection of the beam increases slightly with increased load velocity but increases significantly with reduced shear modulus of subgrade at a given velocity.The maximum deflection of a beam resting on a Pasternak foundation is much smaller than that of a beam on a Winkler foundation.

Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.

New Damage-locating Method for Bridges Subjected to a Moving Load

A new damage-locating method for bridges subjected to a moving load is presented, and a new ‘moving load dam- age-locating indicator’ (MLDI) is introduced. A vehicle is modeled as a moving load, the bridge is simplified as an Euler-Bernoulli beam, and the damage is simulated by a reduction of stiffness properties of the elements. The curvature and MLDI values at each node of the baseline model (undamaged) and the damage model are computed respectively. Then the damage or damages can be located from a sudden change of the MLDI value. The feasibility and effectiveness of the proposed method are validated by nu- merical simulation. The results indicate that the method is effective, being able to not only locate a single damage accurately, but also locate multiple damages in simply-supported bridges, including multiple damages in continuous bridges. The results also indicate that the MLDI can accurately locate damages under 5% measurement noise.

Aerodynamic problems of cable-stayed bridges spanning over one thousand meters

The elongating of cable-stayed bridge brings a series of aerodynamic problems. First of all,geometric nonlinear effect of extreme long cable is much more significant for cable-stayed bridge spanning over one thousand meters. Lateral static wind load will generate additional displacement of long cables,which causes the decrease of supporting rigidity of the whole bridge and the change of dynamic properties. Wind load,being the controlling load in the design of cable-stayed bridge,is a critical problem and needs to be solved. Meanwhile,research on suitable system between pylon and deck indicates fixed-fixed connection system is an effective way for improvement performance of cable-stayed bridges under longitudinal wind load. In order to obtain aerodynamic parameters of cable-stayed bridge spanning over one thousand meters,identification method for flutter derivatives of full bridge aero-elastic model is developed in this paper. Furthermore,vortex induced vibration and Reynolds number effect are detailed discussed.

Experimental and Computational Investigation of Hybrid FRP Bonded-Reinforced Concrete Beams under Cyclic Loading

Although several experimental and numerical studies have been carried out on the shear capacity of RC beams retrofitted by carbon or glass fibre-reinforced polymers, there has been little work on hybrid FRP sheet applications, particularly under cyclic loading. In the present research, five RC beams were constructed, and four of which were retrofitted using various schemes of FRP sheets. All beams were subjected to quasi-static cyclic loading in an attempt to represent the effect repetitive loading. The ultimate load, and deflection response at mid-span of the beams were measured and compared with predictions of a computational model based on finite element analysis. Experimental results demonstrated that hybrid applications of FRP sheets can improve the shear performance of retrofitted RC beams and increase the ultimate strain of the FRP sheets at failure. The results of the computational model were in reasonable agreement with the corresponding experimental results.

Superposability of unsteady aerodynamic loads on bridge deck sections

The 2-dimensional unsteady aerodynamic forces,in the context of both a thin airfoil where theory of potential flow is always applicable and a bluff bridge-deck section where separated flow is typically induced,are investigated from a point of view of whether or not they conform to the principle of linear superposition in situations of various structural motions and wind gusts.It is shown that some basic preconditions that lead to the linear superposability of the unsteady aerodynamic forces in cases of thin airfoil sections are no longer valid for a bluff section.Theoretical models of bridge aerodynamics such as the one related to flutter-buffeting analysis and those concerning aerodynamic admittance(AA)functions,however,necessitate implicitly this superposability.The contradiction revealed in this work may throw light on the perplexing problem of AA functions pertaining to the description of buffeting loads of bridge decks.Some existing theoretical AA models derived from flutter derivatives according to interrelations valid only for thin airfoil theories,which have been employed rather extensively in bridge aerodynamics,are demonstrated to be illogical.Finally,with full understanding of the preconditions of the applicability of linear superposability of the unsteady aerodynamic forces,suggestions in regard to experiment-based AA functions are presented.

Dynamic Response on Free-Free Beam in Driving Point and Transfer Mobility Measurement under Bending Load

This paper aims to present the experimental result obtained from dynamic response on flee-flee beam in driving point and transfer mobility analysis using impact test method using hammer tips that are steel, plastic and rubber. The 8630C accelerometer and analyzer is used for data logging and for the analysis, the plastic hammer tip is chosen. The analytical and the experimental value then are compared for the free-free beam natural frequency, damping ratio, and stiffness value. As a result, the highest percentage error for natural frequency is approximated to 2.7%, the damping ratio is approximated to 3.115 × 10^-3 and the stiffness value gives the major different between the experiment value and theoretical value. Finally, this method can be used to determine the properties of a structure such as natural frequency, mode shapes, damping ration and stiffness, respectively.

Durability of Stress Ribbon Bridge Checked during Loading Test

Stress ribbon bridges have many advantages and became recently more popular mostly because of their versatile form, slender decks giving a light aesthetic impression and durability assured by post tensioned concrete. The paper presents the first in Poland stress Ribbon Bridge constructed last year. A static and dynamic analyse of the model is presented as well as construction solutions which were used to achieve the highest durability. The bridge was checked during static and dynamic load test. The results of this prove test were compared with results obtained from examination and study of other different bridge structures. It confirmed that the bridge has good dynamic resistance and greater stiffness than assumed in the design.

Preliminary Estimation of Torsion of Curved Bridges Subjected to Earthquake Loading

This paper focuses on the seismic response of the curved and post-tensioned concrete box girder bridges. More specifically, it investigates how the curvature influences the response of a bridge subjected to earthquake. Parametric analysis of different radius of curvature is performed and the internal forces, torsion moment, axial and shear along the bridge are calculated. Two types of connections are investigated, the monolithic connection and deck connection with bents and abutments with rubber bearing. The response spectrum seismic analysis was performed. The models were designed, according to the provisions of EC8-part 2, EC2 and the Greek regulations E39/99. Diagrams relating the curvature with the torsion moment have been obtained from the results of parametric analysis. These diagrams could be used by engineers for preliminary design of such kind of bridges.

Cost Impact of Increasing Heavy Vehicle Loads on Bridges

This study aimed to investigate the cost impact of meeting the increase in freight demand by doubling the truck weight （AS 1 ）, doubling the traffic volume （AS2）, or legalizing a new-proposed-truck of 97-kip weight instead of the currently legal 80-kip truck （AS3）. The State of Michigan＇s average daily traffic database of year 2001 has been used as a case study. The study was applied only on the very common US Bridge with RC （reinforced concrete） deck over steel girder. Sampling criteria also includes the age of the bridges. The study covered the four-cost-impact categories provided by the NCHRP （National Cooperative Research Program）. The current truck weight and double traffic volume （AS2） show the best scenario to meet the increase in freight demand. However, doubling the truck weight with the current traffic volume （AS 1） was the worst scenario. The use of the proposed 97-kip truck with the current traffic volume （AS3） compromises both, meeting the increase in freight demand and the cost impact.

Elasticity solution of laminated beams subjected to thermo-loads

According to the two-dimensional(2-D) thermo-elasticity theory, the exact elasticity solution of the simply supported laminated beams subjected to thermo-loads was studied. An analytical method was presented to obtain the temperature, displacement and stress fields in the beam. Firstly, the general solutions of temperature, displacements and stresses for a single-layered simply supported beam were obtained by solving the 2-D heat conduction equation and the 2-D elasticity equations, respectively. Then, based on the continuity of temperature, heat flux, displacements and stresses on the interface of two adjacent layers, the formulae of temperature, displacements and stresses between the lowest layer and the top layer of the beam were derived out in a recurrent manner. Finally, the unknown coefficients in the solutions were determined by the use of the upper surface and lower surface conditions of the beam. The distributions of temperature, displacement and stress in the beam were obtained by substituting these coefficients back to the recurrence formulae and the solutions. The excellent convergence of the present method has been demonstrated and the results obtained by the present method agree well with those from the finite element method. The effects of surface temperatures, thickness, layer number and material properties of the plate on the temperature distribution were discussed in detail. Numerical results reveal that the displacements and stresses monotonically increase with the increase of surface temperatures. In particular, the horizontal stresses are discontinuous at the interface.

Seismic Behavior of Confined RC ColumnComposite Beam Joints

In order to evaluate the seismic behavior of confined RC column-composite beam joints, five interior joints were tested under low cyclic reversed load. The weakening extent of flanges, the number of studs, and whether to reinforce weakened flanges were used as parameters in designing these five joints. Failure characteristics, hysteretic curves, skeleton curves, ductility, energy dissipation, strength degradation, and stiffness degradation were analyzed. The test results revealed that the steel beam flanges in the joints were equivalent to the tie rod. Weakened flanges resulted in poor seismic behavior; however, the seismic behavior could be improved by increasing studs and reinforcing weakened flanges. The joint steel plate hoops, equivalent to stirrups, did not yield when the maximum load was reached, but yielded when the failure load was reached for the joints with shear failure. Increasing stud-type joints and reinforcing flange-type joints ensured good seismic behavior and met project requirements. Based on the experimental results, the failure mechanism of the joints was discussed, and the shear capacity equations of the joints was presented.

Reinforcement and numerical analysis on the corbel of a halfthrough arch bridge

Corbels support the crossbeams of half-through arch bridges. They are prone to cracking easily due to their characteristics and complicated loading conditions. Based on a practical diagnosis of a bridge crossbeam, we bonded steel plates onto bridge corbels to strengthen them. We carried out a numerical analysis on the effectiveness of the reinforcement by using the commercial sof^are ANSYS. The numerical analysis shows that the stresses near the section break increased slightly, but the variation amplitude was small and all the stresses were within an allowable range. The loading test indicates that it is feasible to strengthen the corbel with vertical bonded steel plates. Therefore, the reinforcement is effective and economical. This reinforcement method is suitable for this type of corbel and can be applied in similar cases.

Vertical load capacities of roof truss cross members

Trusses used for roof support in coal mines are constructed of two grouted bolts installed at opposing forty-five degree angles into the roof and a cross member that ties the angled bolts together. The load on the cross member is vertical, which is transverse to the longitudinal axis, and therefore the cross member is loaded in the weakest direction. Laboratory tests were conducted to determine the vertical load capacity and deflection of three different types of cross members. Single-point load tests, with the load applied in the center of the specimen and double-point load tests, with a span of 2.4 m, were conducted. For the single-point load configuration, the yield of the 25 mm solid bar cross member was nominally 98 kN of vertical load, achieved at 42 cm of deflection. For cable cross members, yield was not achieved even after 45 cm of deflection. Peak vertical loads were about 89 kN for 17 mm cables and67 kN for the 15 mm cables. For the double-point load configurations, the 25 mm solid bar cross members yielded at 150 kN of vertical load and 25 cm of deflection. At 25 cm of deflection individual cable strands started breaking at 133 and 111 kN of vertical load for the 17 and 15 mm cable cross members respectively.

Strengthening of Concrete Box Girder Bridges under Close-in Detonations

The response of a bridge superstructure under blast loading might depend largely on the extent of the local damage experienced due to close-in explosion threats. This paper investigates the local and structural response of box girder bridge decks strengthened using CFRP （carbon fiber reinforced polymers） under close-in detonations. Due to the lack of experimental research on this topic, the study is conducted using the explicit finite element computer program LS-DY-NA. The numerical study will be verified using the results of strengthened reinforced concrete slabs under field detonations. The blast load was assumed to be detonated above the bridge deck. The key parameters investigated are the charge size, and the strengthening location on the deck. This paper will present the results of this investigation and provides recommendations for predicting the local damage level based on the CFRP strengthening design under blast threat.

Numerical Approach for the Live Load Distribution in Road Bridges

The numerical method for computing the live load distribution coefficients in bridge decks is presented. The grillage analogy for representation of bridge decks is adopted in determining the general behavior under traffic loads. The principles of Maxwell＇s reciprocal theorem are developed in computing live load distribution coefficients and their influence lines. The presented method uses the approach developed in traditional methods of transversal live load distribution but bridge decks are modeled more realistic with the help of well-established grillage analogy. Simple numerical programs for grillage analysis can be used and no special software is needed. While computing the distribution coefficients for a bridge deck the rest of the analysis can be performed with habitual procedures of structural mechanics.